1. Deformable Mirrors Lecture 8
Claire Max
Astro 289, UCSC
January 31, 2013

2. Before we discuss DMs: Two digressions
Correction of SNR discussion from Lecture 7
Some great images of a curvature AO system from Richard Ordonez, University of Hawaii

3. Correction to signal to noise ratio discussion from Lecture 7
Total signal to noise ratio:
where S is the average photo-electron flux, tint is the time interval of the measurement, BSky is the electrons per pixel per sec from the sky background, D is the electrons per pixel per sec due to dark current, and R is the readout noise per pixel.
Poisson noise
Sky bkgnd
Dark current
Read noise

4. CCD-based wavefront sensors are usually dominated by read noise
Read-noise dominated:
If there are lots of photons but read noise is high, SNR is

5. Curvature WF Sensor Array Mounted in Holder, Along with Fiber Cables
Lenslet Array
From presentation by Richard Ordonez, U. of Hawaii Manoa

6. Avalanche photodiode array
Curvature WF Sensor
Collects information about phase curvature and edge-slope data
S = I-E
I+E
S = signal
I = intra focal images
E= Extra focal images
The wavefront sensor acts as the eyes of the system. The wavefront sensor works by the comparing the intensity differences from intra and extra focal images collected by the lenslet array (shown top left) and avalanche photo diodes (shown top right). This information is sufficient enough to create a signal S which contains information about phase curvature and edge boundary data. The data collected is transformed to a correction matrix via a computer and control voltages are sent to the Deformable mirror.
Avalanche photodiode array
Lenslet array
From presentation by Richard Ordonez, U. of Hawaii Manoa

7. Outline of Deformable Mirror Lecture
Performance requirements for wavefront correction
Types of deformable mirrors
Actuator types
Segmented DMs
Continuous face-sheet DMs
Bimorph DMs
Adaptive Secondary mirrors
MEMS DMs
(Liquid crystal devices)
Summary: fitting error, what does the future hold?

8. Deformable mirror requirements: r0 sets number of degrees of freedom of an AO system
Divide primary mirror into “subapertures” of diameter r0
Number of subapertures ~ (D / r0)2 where r0 is evaluated at the desired observing wavelength

9. Overview of wavefront correction
Divide pupil into regions of ~ size r0 , do “best fit” to wavefront. Diameter of subaperture = d
Several types of deformable mirror (DM), each has its own characteristic “fitting error”
σfitting2 = μ ( d / r0 )5/3 rad2
Exactly how large d is relative to r0 is a design decision; depends on overall error budget

10. DM requirements (1) Dynamic range: stroke (total up and down range)
Typical “stroke” for astronomy depends on telescope diameter:
± several microns for 10 m telescope
± microns for 30 m telescope
± For microns for retinal imaging
Temporal frequency response:
DM must respond faster than a fraction of the coherence time τ0
Influence function of actuators:
Shape of mirror surface when you push just one actuator (like a Greens’ function)
Can optimize your AO system with a particular influence function, but performance is pretty forgiving

11. DM requirements (2) Surface quality: Hysteresis of actuators:
Small-scale bumps can’t be corrected by AO
Hysteresis of actuators:
Repeatability
Want actuators to go back to same position when you apply the same voltage
Power dissipation:
Don’t want too much resistive loss in actuators, because heat is bad (“seeing”, distorts mirror)
Lower voltage is better (easier to use, less power dissipation)
DM size:
Not so critical for current telescope diameters
For 30-m telescope need big DMs: at least 30 cm across
Consequence of the Lagrange invariant

12. Types of deformable mirrors: conventional (large)
Segmented
Made of separate segments with small gaps
“Continuous face-sheet”
Thin glass sheet with actuators glued to the back
Bimorph
2 piezoelectric wafers bonded together with array of electrodes between them. Front surface acts as mirror.

13. Types of deformable mirrors: small and/or unconventional (1)
Liquid crystal spatial light modulators
Technology similar to LCDs
Applied voltage orients long thin molecules, changes n
Not practical for astronomy
MEMS (micro-electro-mechanical systems)
Fabricated using micro-fabrication methods of integrated circuit industry
Potential to be inexpensive

14. Types of deformable mirrors: small and/or unconventional (2)
Membrane mirrors
Low order correction
Example: OKO (Flexible Optical BV)
Magnetically actuated mirrors
High stroke, high bandwidth
Example: ALPAO

15. Typical role of actuators in a conventional continuous face-sheet DM
Actuators are glued to back of thin glass sheet (has a reflective coating on the front)
When you apply a voltage to the actuator (PZT, PMN), it expands or contracts in length, thereby pushing or pulling on the mirror V

16. Types of actuator: Piezoelectric
Piezo from Greek for Pressure
PZT (lead zirconate titanate) gets longer or shorter when you apply V
Stack of PZT ceramic disks with integral electrodes
Displacement linear in voltage
Typically 150 Volts ⇒ Δx ~ 10 microns
10-20% hysteresis (actuator doesn’t go back to exactly where it started)

17. Types of actuator: PMN Lead magnesium niobate (PMN) Electrostrictive:
Material gets longer in response to an applied electric field
Quadratic response (non-linear)
Can “push” and “pull” if a bias is applied
Hysteresis can be lower than PZT in some temperature ranges
Both displacement and hysteresis depend on temperature (PMN is more temperature sensitive than PZT)
Good reference (figures on these slides):

18. Segmented deformable mirrors: concept
Each actuator can move just in piston (in and out), or in piston plus tip-tilt (3 degrees of freedom)
Fitting error:
σfitting2 = μ ( d/r0 )5/3
Piston only: μ = 1.26
3 degrees of freedom:
μ = 0.18
actuators
Light
Piston only
Piston+tip+tilt

19. Segmented deformable mirrors: Example
NAOMI (William Herschel Telescope, UK): 76 element segmented mirror
Each square segment mirror is mounted on 3 piezos, each of which has a strain gauge
Strain gauges provide independent measure of movement, are used to reduce effects of hysteresis

20. Continuous face-sheet DMs: Design considerations
Facesheet thickness must be large enough to maintain flatness during polishing, but thin enough to deflect when pushed or pulled by actuators
Thickness also determines “influence function”
Response of mirror shape to “push” by 1 actuator
Thick face sheets ⇒ broad influence function
Thin face sheets ⇒ more peaked influence function
Actuators have to be stiff, so they won’t bend sideways

21. Palm 3000 High-Order Deformable Mirror: 4356 actuators!
Credit: A. Bouchez
Xinetics Inc. for Mt. Palomar “Palm 3000” AO system

22. Palm 3000 DM Actuator Structure
Credit: A. Bouchez
Actuators machined from monolithic blocks of PMN
6x6 mosaic of 11x11 actuator blocks
2mm thick Zerodur glass facesheet
Stroke ~1.4 µm without face sheet, uniform to 9% RMS.
Prior to face sheet bonding

23. Palm 3000 DM: Influence Functions
Credit: A. Bouchez
Influence function: response to one actuator
Zygo interferometer surface map of a portion of the mirror, with every 4th actuator poked

24. Bimorph mirrors are well matched to curvature sensing AO systems
Electrode pattern shaped to match sub-apertures in curvature sensor
Mirror shape W(x,y) obeys Poisson Equation
Credit: A. Tokovinin

25. Bimorph deformable mirrors: embedded electrodes
Credit: CILAS
Electrode Pattern
Wiring on back
ESO’s Multi Application Curvature Adaptive Optics (MACAO) system uses a 60-element bimorph DM and a 60-element curvature wavefront sensor
Very successful: used for interferometry of the four 8-m telescopes

26. Deformable Secondary Mirrors
Pioneered by U. Arizona and Arcetri Observatory in Italy
Developed further by Microgate (Italy)
Installed on:
U. Arizona’s MMT Upgrade telescope
Large binocular telescope (Mt. Graham, AZ)
Magellan Clay telescope, Chile
Future: VLT laser facility (Chile)

27. Cassegrain telescope concept
Secondary mirror

28. Adaptive secondary mirrors
Make the secondary mirror into the “deformable mirror”
Curved surface ( ~ hyperboloid) ⇒tricky
Advantages:
No additional mirror surfaces
Lower emissivity. Ideal for thermal infrared.
Higher reflectivity. More photons hit science camera.
Common to all imaging paths except prime focus
High stroke; can do its own tip-tilt
Disadvantages:
Harder to build: heavier, larger actuators, convex.
Harder to handle (break more easily)
Must control mirror’s edges (no outer “ring” of actuators outside the pupil)

29. General concept for adaptive secondary mirrors (Arizona, Arcetri, MicroGate)
Voicecoil actuators are located on rigid backplate or “reference body”
Thin shell mirror has permanent magnets glued to rear surface; these suspend the shell below the backplate
Capacitive sensors on backplate give an independent measurement of the shell position

30. Diagram from MicroGate’s website

31. Adaptive secondary mirror for Magellan Telescope in Chile
PI: Laird Close, U. Arizona

32. Deformable secondaries: embedded magnets
LBT DM: magnet array LBT DM: magnet close-up
Adaptive secondary DMs have inherently high stroke: no need for separate tip-tilt mirror!

33. It Works! 10 Airy rings on the LBT!
Strehl ratio > 80%

34. Concept Question
Assume that its adaptive secondary mirror gives the 6.5 meter MMT telescope’s AO system twice the throughput (optical efficiency) as conventional AO systems.
Imagine a different telescope (diameter D) with a conventional AO system.
For what value of D would this telescope+AO system have the same light-gathering power as the MMT?

35. Cost scaling will be important for future giant telescopes
Conventional DMs
About $1000 per degree of freedom
So $1M for 1000 actuators
Adaptive secondaries cost even more.
VLT adaptive secondaries in range $12-14M each
MEMS (infrastructure of integrated circuit world)
Less costly, especially in quantity
Currently ~ $100 per degree of freedom
So $100,000 for 1000 actuators
Potential to cost 10’s of $ per degree of freedom

36. What are MEMs deformable mirrors?
MEMS: Micro-electro-mechanical systems
A promising new class of deformable mirrors, MEMs DMs, has recently emerged
Devices fabricated using semiconductor batch processing technology and low power electrostatic actuation
Potential to be less expensive ($10 - $100/actuator instead of $1000/actuator)
4096-actuator MEMS deformable mirror. Photo courtesy of Steven Cornelissen, Boston Micromachines

37. One MEMS fabrication process: surface micromachining1 2 3

38. Boston University MEMS Concept
Electrostatically actuated diaphragm
Attachment post
Membrane mirror
Fabrication: Silicon micromachining (structural silicon and sacrificial oxide)
Actuation: Electrostatic parallel plates
Continuous mirror
Boston University
Boston MicroMachines

39. Boston Micromachines: 4096 actuator MEMS DM
Mirror for Gemini Planet Imager
4096 actuators
64 x 64 grid
About 2 microns of stroke

40. MEMS testing at Laboratory for Adaptive Optics: very promising
Credit: Morzinski, Severson, Gavel, Macintosh, Dillon (UCSC)

41. Another MEMS concept: IrisAO’s segmented DM
Each segment has 3 degrees of freedom
Now available with 100’s of segments
Large stroke: > 7 microns

42. IrisAO PT489 DM
163 segments, each with 3 actuators (piston+tip+tilt)
Hexagonal segments, each made of single crystal silicon
8 microns of stroke (large!)

43. Approach of Prof. Joel Kubby at UCSC
Goal: higher stroke

44. Issues for all MEMS DM devices
“Snap-down”
If displacement is too large, top sticks to bottom and mirror is broken (can’t recover)
Robustness not well tested on telescopes yet
Sensitive to humidity (seal using windows)
Will there be internal failure modes?
Defect-free fabrication
Current 4000-actuator device still has quite a few defects

45. Concept Question
How does the physical size (i.e. outer diameter) of a deformable mirror enter the design of an AO system?
Assume all other parameters are equal: same number of actuators, etc.

46. Fitting errors for various DM designs
σfitting2 = μ ( d / r0 )5/3 rad2
DM Design μ Actuators / segment
Piston only,
square segments
Piston+tilt,
Square segments
Continuous DM

47. Consequences: different types of DMs need different actuator counts, for same conditions
To equalize fitting error for different types of DM, number of actuators must be in ratio
So a piston-only segmented DM needs
( 1.26 / 0.28 )6/5 = 6.2 times more actuators than a continuous face-sheet DM!
Segmented mirror with piston and tilt requires 1.8 times more actuators than continuous face-sheet mirror to achieve same fitting error: N1 = 3N2 ( 0.18 / 0.28 )6/5 = 1.8 N2

48. Summary of main points Deformable mirror acts as a “high-pass filter”
Can’t correct shortest-wavelength perturbations
Different types of mirror have larger/smaller fitting error
Design of DMs balances stiffness and thickness of face sheet, stroke, strength of actuators, hysteresis, ability to polish mirror with high precision
Large DMs have been demonstrated (continuous face sheet, adaptive secondary) for ~ actuators
MEMs DMs hold promise of lower cost, more actuators
Deformable secondary DMs look very promising